Reliability Modelling

Reliability Modelling : a Statistical Approach

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Reliability is an essential concept in mathematics, computing, research, and all disciplines of engineering, and reliability as a characteristic is, in fact, a probability. Therefore, in this book, the author uses the statistical approach to reliability modelling along with the MINITAB software package to provide a comprehensive treatment of modelling, from the basics through advanced modelling techniques. The book begins by presenting a thorough grounding in the elements of modelling the lifetime of a single, non-repairable unit. Assuming no prior knowledge of the subject, the author includes a guide to all the fundamentals of probability theory, defines the various measures associated with reliability, then describes and discusses the more common lifetime models: the exponential, Weibull, normal, lognormal and gamma distributions. She concludes the groundwork by looking at ways of choosing and fitting the most appropriate model to a given data set, paying particular attention to two critical points: the effect of censored data and estimating lifetimes in the tail of the distribution. The focus then shifts to topics somewhat more difficult: * the difference in the analysis of lifetimes for repairable versus non-repairable systems and whether repair truly "renews" the system * methods for dealing with system with reliability characteristic specified for more than one component or subsystem * the effect of different types of maintenance strategies * the analysis of life test data The final chapter provides snapshot introductions to a range of advanced models and presents two case studies that illustrate various ideas from throughout the more

Product details

  • Paperback | 272 pages
  • 152 x 226 x 16mm | 421.84g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 12 black & white tables
  • 1584880147
  • 9781584880141
  • 1,901,460

Review quote

"This is a lucid introduction to many important ideas in reliability. In describing the various models and techniques the author includes plenty of practical advice about their usuage. Frequent and well-developed examples illustrate and extend the techniques and there are two brief case studies at the end of the book. By studying these examples carefully, the student will learn much about the difficult art of formulating useful models." --Biometrics, June 2000show more

Table of contents

BASIC CONCEPTS Introduction Events and Probability Rules of Probability Dependent Events Random Variables and Probability Distributions The Reliability Function The Hazard Function Expectation COMMON LIFETIME MODELS Introduction The Poisson Process The Weibull Distribution The Gumbel Distribution The Normal and Lognormal Distributions The Gamma Distribution The Logistic and Log Logistic Distributions The Pareto Distribution Order Statistic and Extreme Value Distributions MODEL SELECTION Introduction Non-Parametric Estimation of R(t) and h(t) Censoring Kaplan-Meier Estimator Graphical Methods Straight Line Fitting Weibull Plotting Normal Plotting Other Model Family Plots Comparison of Distributions MODEL FITTING Parameter Estimation The Variance of Estimators Confidence Interval Estimates Maximum Likelihood Estimating Quantities Estimation Methods Using Sample Moments General Probability Plots Goodness of Fit Pearson's Chi-squared Test Kolmogorov-Smirnov Test Tests for Normality A-squared and W-squared Tests Stabilized Probability Plots Censored Data REPAIRABLE SYSTEMS Introduction Graphical Methods Testing for Trend Repair Time Maintainability and Availability Introduction to Renewal Theory Laplace Transforms The Renewal Function Alternating Renewal Processes The Distribution of N(t) SYSTEM RELIABILITY Systems and System Logic Tie and Cut Sets Probability Bounds Fault Trees Failure Over Time Redundancy Quorum or m-out-of-n Systems Analysis of Systems Using State Spaces Mean Time to Fail (MTTF) Considerations Due to "Switching" Common Cause Failures MODELS FOR FUNCTIONS OF RANDOM VARIABLES Combinations and Transformations of Random Variables Expectations of Functions of Random Variables Approximations for E[g(x)] and V[g(x)] Distribution of a Function of Random Variables Probabilistic Engineering Design Stress and Strength Distributions Interference Theory and Reliability Computations Normally Distributed Stress and Strength Safety Factors and Reliability Graphical Approach for Empirically Determined Distributions MAINTENANCE STRATEGIES Maintained Systems Availability Markovian Systems Mean Time between Failures (MTBF) Age Replacement Scheduled Maintenance Systems with Failure Detection/Fail Safe Devices Down-Time Distributions LIFE TESTING AND INFERENCE Life Test Plans Prediction of Time on Test Inference for the Exponential Distribution The Effect of Data Rounding Parametric Reliability Bounds Likelihood-Based Methods The Likelihood Ratio Test Binomial Experiments Non-Parametric Estimation and Confidence Intervals for R(t) Estimating System Reliability from Subsystem Test Data Accelerated Testing ADVANCED MODELS Covariates Proportional Hazards Models Accelerated Life Models Mixture Models Competing Risks Dependent Failures Load-Sharing Systems Bayesian Reliability Case Studies USEFUL MATHEMATICAL TECHNIQUES Partial Fractions Series Taylor Expansions Newton-Raphson Iteration Numerical Integration Matrix Algebra The Principle of Least Squaresshow more

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